Sen. Jeff Sessions (R-Ala.) ranking Republican on the Senate Budget Committee, speaks with Sen. Jim DeMint (R-S.C.) a member of the Senate Banking Committee and the Joint Economic Committee (r.) on Capitol Hill in Washington, on June 29.

Washington — As President Obama renewed calls for a “balanced approach” to deficit talks, Senate Republicans on Wednesday launched a bid to get Congress to vote on a balanced budget amendment to the US Constitution by mid-July – ahead of a vote on Mr. Obama's request to raise the national debt limit.

The political odds are formidable. While all 47 Senate Republicans back the measure, at least 20 Democrats would be needed to meet the two-thirds majority threshold. So far, no Democrat has endorsed it. Even if Congress were to approve the amendment, it must be ratified by three-fourths of the states – a process that can take up to seven years.

But even a failed drive for a constitutional amendment gives Republicans a rallying point in the last crucial weeks of negotiation with the White House over raising the national debt limit.

“What Washington needs isn’t more revenue but a “spending straightjacket,” said Republican leader Mitch McConnell of Kentucky in a floor speech on Wednesday. “Senators can talk all day long about the importance of balancing the books and living within our means. A vote in favor of the Balanced Budget Amendment will show that they mean it,” he added. “A vote against it will show that they don’t.”

Freshman Sen. Marco Rubio (R) of Florida said that a balanced budget amendment would “handcuff out-of-control politicians.” “We can no longer afford it, and we owe it to the next generation of Americans to make this right,” he said in a statement.

Mr. Obama pressed Republicans on their refusal to consider tax increases, at a press conference on Wednesday. “You can’t reduce the deficit to the levels that it needs to be reduced without having some revenue in the mix,” he said. These include curtailing tax breaks for millionaires and billionaires, gas and oil companies, hedge fund managers, and other corporate loopholes.

GOP senators say they will take the case for such an amendment to voters when they return home next week. At least 65 percent of Americans favor a balanced budget amendment, according to recent polls.

“It’s no surprise why this amendment has so much support,” Sen. Mike Johanns (R) of Nebraska said on the floor on Wednesday. “Because to the average family, it’s what they do every day.”

House Republicans say they will bring to the floor their own version of a balanced budget amendment before a vote to raise the debt ceiling. The House version would require that the government balance its budget every year, limit spending to 20 percent of gross domestic product, and raise taxes only with consent of a three-fifths supermajority. The Senate GOP proposal would limit spending to 18 percent of GDP and require a two-thirds supermajority to raise taxes.

That threshold makes it “virtually impossible to raise revenues,” including closing tax loopholes, according to a June 6 report by the Center on Budget and Policy Priorities, a research group that assesses the impact of fiscal policy on low- and moderate-income households.

Last week, some 40 conservative groups launched a drive to get candidates for federal office to commit to refusing to vote for a debt limit increase unless a constitutional balanced budget amendment, along with spending cuts and caps, is part of the deal.

“We can’t keep taking out new credit cards to pay off the ones we’ve maxed out,” said Sen. Jim DeMint (R) of South Carolina in a statement on Wednesday. “It’s time to pass a balanced budget amendment and force Washington to stop spending more than we’re taking in.”

Senator DeMint is one of 12 GOP senators to have signed a pledge not to vote to increase the national debt limit without also passing a balanced budget amendment. That means 35 Republican senators have not signed such a pledge.

Senate Democrats say they are seeing other rifts in GOP ranks that could help produce a deal on raising the country's debt limit. So far, GOP leaders have drawn a line on taxes. But 34 Republicans, including Senate leader McConnell, last week voted to end subsidies for the ethanol industry.

“It makes no sense for leader McConnell to, on the one hand, say he agrees that ethanol subsidies are wasteful but then … stick to an ideological, way-out-there principle that we can’t eliminate that subsidy in the debt-limit deal,” said Sen. Charles Schumer (D) of New York at a briefing with reporters Wednesday.

"We're hitting crunch time in these debt-ceiling talks. If we're going to reach a grand bargain, neither side can cling to its ideological positions any longer," he said.